I actually went down a little rabbit hole yesterday looking for Mormon prayer texts, and they seem quite hard to find. No doubt that is at least in part because of the Mormon misconception concerning the Bible's warning against vain repetitions (which is hardly a misconception unique to them), so it seems that most of their prayers are extemporaneous (there's obviously nothing like a Mormon Book of the Hours), though following a kind of generic Protestant-seeming pattern, a la "Father, we just wanna..." (but more formal sounding).
Among my favorites of what I found (presented not to mock, but to educate by showing actual examples of what Mormons may pray):
"Heavenly Father, we thank thee for this day, and thank thee for the moisture we have received. Please bless the refreshments, that they will nourish and strengthen our bodies..." (from
7 Prayer Phrases Mormons Could Say in Their Sleep (+What We Should Maybe Be Praying for Instead) | LDS Living)
Dear Father in Heaven,
I come before Thee in grateful prayer tonight, thanking Thee for my life and health, for agency, and for a future. Please accept my gratitude for sending Thy Son. I pray that I will follow His example of kindness, forgiveness, and purity.
Dear Father in Heaven, make me a kinder neighbor, a more diligent student, a more productive employee, and a more loyal citizen. Instill in my heart a greater love for all Thy children, and make me an example of the believers. Forgive my laziness, hypocrisy and offense.
I pray for my dear wife. Preserve her and uplift her. Bless her richly for her faith, her pure heart and her hard work. Make me a more reliable husband. Bless all our children, nieces and nephews, that they might recognize the influence of Thy Spirit, and know Thee. Protect them and guide them in their growth and education. Soften their feelings and give them good judgment, and success and achievement. I pray for our parents and their health and longevity; and my two sisters.
I pray for our national leaders, that they may make their decisions in justice and righteousness, that peace and prosperity may prevail at home and abroad. I pray for civil discourse and a culture of respect. I pray for peace in our homes and families, and for safety in schools and neighborhoods.
Send a special blessing on those who are seeking employment, that they might use their talents and support their families. Please intervene in the Gulf of Mexico to stop the oil spill. Please bless the peoples in war-torn areas like Iraq and Afghanistan, that they might turn from violence and oppression.
I thank Thee for the infinite Atonement of Thy Son, for forgiveness and reconciliation, for His perfect example. I thank Thee for restoring the gospel to the earth through the Prophet Joseph Smith, and for our prophet today, President Thomas S. Monson. Please continue to guide and inspire him and his associates. I thank Thee for the Bible and the Book of Mormon, for the Church and its teachings. I pray for those who are seeking the gospel, that they may find the truth. Protect the missionaries throughout the world, and bring them home safely.
(from an individual Mormon's
answer to this question on Quora)
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While there is good stuff to be found at both those links (certainly nobody here would say that it is somehow wrong to pray for safety in the world, or a better marriage, or things like these), there is obviously nothing that rises to the level of time-honored, sanctifying Christian prayer in the name of the Father, and of the Son, and of the Holy Spirit, the One God.